A properly braced cab should not display this behavior (granted, only so much you can do with that thin material, but a tensionned t-b brace should be in the equation somewhere, imo)...the box should not be that "live". That said, expect when all sorted out, that the cab will sound a bit different in the end for it. How thick is the baffle?

Also, that amount of vibration is doing none of your heads any favors (including the one on your shoulders), so you need to address this soon.
Also, is the Duratex glossy? That might be part of the issue.

I too really want to see video. But only with a spotter for the head...